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3

You may be interested in the paper G. Aronsson, L. C. Evans, Y. Wu. Fast/slow diffusion and growing sandpiles, Journal of Differential Equations, volume 131, number 2, 1996, pages 304–335 This paper uses the $p$-laplacian $\operatorname{div} (|\nabla u|^{p-2}| \nabla u)$ to model the diffusion of sand particles. If you want to know more about this ...


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I'd be surprised if it is a Bell curve. But sand-piles are a research area, try searching "self organized criticality".


0

No. Speed of light in Vacuum isn't dependent on Solar System's motion. It's a constant. It'd be same even if the motion wasn't there. Due to your question type problems, we've even calibrated our scales to create Relativistic Physics.


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No the speed of light in vaccuum is an absolute constant $c$ = 299 792 458 m/s The way to add up relativistic speeds is: $u' = \frac{u-v}{1-\frac{uv}{c^2}}$ to account for the constancy of the speed of light You cannot simply add them up. Edit: This also applies to normal everyday speeds. The reason we don't use this formula is because the speeds we are ...


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Calculating the effect of acceleration in special relativity is straightforward, but I suspect the algebra is a bit much at high school level. See John Baez's article on the Relativistic Rocket for a summary, or see Chapter 6 of Gravitation by Misner, Thorne and Wheeler for a more detailed analysis. When you're first introduced to SR you tend to be told ...


3

If you are the observer and you are observing a car move in front of you, then the clock in the car will appear to move slower than the clock in your reference frame and the length of the car will appear to be contracted to you in the direction of motion. All these effects get magnified as the velocity of the car approaches that of light. In the same way, ...


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Everything remains relativistic. However, the variation between the Newtonian and Einstein relativity is of the order of $v^2/c^2$. So when this number drops below observable error, you can't tell the difference.


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If you leave earth at age 30 and live for 30 years near a black hole, time will pass more slowly for you and normal for the people on the earth. I don't know the exact age you will be when you spend 30 years near a black hole, but when you return to earth you will be younger than others who had the same age as yours when you left. In other words, others at ...


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For any observer observing two events, $E_1$ and $E_2$, the Lorentz factor is: $$ \gamma = \frac{\Delta t}{\Delta \tau} \tag{1}$$ where $\Delta t$ is the time interval measured by the observer, i.e. $t_2 - t_1$, and $\Delta \tau$ is the proper time difference calculated by the observer. To see this consider the example you give of our observer watching a ...


5

You can define the age of the universe roughly as the proper time for a hypothetical observer who is comoving with the galaxies and not too near a strongly gravitating object. This is imprecise because the galaxies are themselves moving around and the age would depend on exactly the worldline of the observer and how it moved to avoid heavy objects that ...



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